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A new method of improving performance of coaxial gyrotron resonators is presented. It is based on the use of a corrugated insert with variable depth of longitudinal corrugations. Such an insert mitigates the mode competition problem in oversized cavities and redistributes heat losses along the axial direction. The method is illustrated in the case of the resonator used in the coaxial cavity gyrotron operating at Forschungszentrum Karlsruhe.